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Transformations for multivariate statistics

Marsh, P (2004) Transformations for multivariate statistics. Econometric Theory. pp. 963-987. ISSN 0266-4666

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Abstract

This paper derives transformations for multivariate statistics that eliminate asymptotic skewness, extending the results of Niki and Konishi (1986, Annals of the Institute of Statistical Mathematics 38, 371-383). Within the context of valid Edgeworth expansions for such statistics we first derive the set of equations that such a transformation must satisfy and second propose a local solution that is sufficient up to the desired order. Application of these results yields two useful corollaries. First, it is possible to eliminate the first correction term in an Edgeworth expansion, thereby accelerating convergence to the leading term normal approximation. Second, bootstrapping the transformed statistic can yield the same rate of convergence of the double, or prepivoted, bootstrap of Beran (1988, Journal of the American Statistical Association 83, 687-697), applied to the original statistic, implying a significant computational saving. The analytic results are illustrated by application to the family of exponential models, in which the transformation is seen to depend only upon the properties of the likelihood. The numerical properties are examined within a class of nonlinear regression models (logit, probit, Poisson, and exponential regressions), where the adequacy of the limiting normal and of the bootstrap (utilizing the k-step procedure of Andrews, 2002, Econometrica 70, 119-162) as distributional approximations is assessed.

Item Type: Article
Copyright, Publisher and Additional Information: © 2004 Cambridge University Press
Keywords: FINITE SAMPLE DISTRIBUTIONS, INFORMATION MATRIX TEST, ASYMPTOTIC EXPANSIONS, ECONOMETRIC ESTIMATORS, EDGEWORTH EXPANSIONS, CRITICAL-VALUES, BOOTSTRAP, APPROXIMATIONS, VALIDITY, THEOREM
Institution: The University of York
Academic Units: The University of York > Economics and Related Studies (York)
Depositing User: Sherpa Assistant
Date Deposited: 19 Aug 2005
Last Modified: 14 Oct 2014 20:28
Published Version: http://dx.doi.org/10.1017/S0266466604205084
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/595

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